Out(Fn)

In mathematics, Out(F_n) is the outer automorphism group of a free group on n generators. These groups are at universal stage in geometric group theory, as they act on the set of presentations with ${\displaystyle n}$ generators of any finitely generated group.^[1] Despite geometric analogies with general linear groups and mapping class groups, their complexity is generally regarded as more challenging, which has fueled the development of new techniques in the field.